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The sides of a parallelogram are 2hati +...

The sides of a parallelogram are `2hati +4hatj -5hatk and hati + 2hatj +3hatk `. The unit vector parallel to one of the diagonals is

A

`(1)/(sqrt(69))(hati+2hatj-8hatk)`

B

`(1)/(69)(hati+2hatj-8hatk)`

C

`(1)/(sqrt(69))(-hati-2hatj+8hatk)`

D

`(1)/(69)(-hati-2hatj+8hatk)`

Text Solution

Verified by Experts

The correct Answer is:
C
Since, `AB+BD=AD`
`BD=AD-AB`
`implies =(hati+2hatj+3hatk)-(2hati+4hatj-5hatk)`
`=-hati-2hatj+8hatk`
Hence, unit vector in the direction of BD is
`(-hati-2hatj+8hatk)/(|-hati-2hatj+8hatk|)=(-hati-2hatj+8hatk)/(sqrt(69))`.
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